Details

Time bar (total: 19.3s)

sample105.0ms

Algorithm
intervals
Results
31.0ms301×body80valid
15.0ms25×body1280valid
10.0ms23×body640valid
4.0ms13×body320valid
2.0ms9×body160valid

simplify2.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01216
12616
26716
324116
4109716
done500016

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
5.0b
(* (* x (pow sin 2.0)) x)
8.5b
(* x (pow sin 2.0))
15.4b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
122×add-exp-log
82×prod-exp
34×add-cbrt-cube
18×pow-to-exp pow-exp
17×add-sqr-sqrt
16×div-exp cbrt-unprod
12×add-cube-cbrt *-un-lft-identity
11×associate-*r* associate-*l*
7×unpow-prod-down
6×pow1
4×cbrt-undiv expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac *-commutative associate-/l* unswap-sqr sqr-pow
1×frac-2neg pow-prod-down clear-num associate-/r* div-inv
Counts
4 → 123
Calls
4 calls:
69.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
28.0ms
(* (* x (pow sin 2.0)) x)
16.0ms
(* x (pow sin 2.0))
78.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.2s

Counts
4 → 12
Calls
4 calls:
403.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
198.0ms
(* (* x (pow sin 2.0)) x)
184.0ms
(* x (pow sin 2.0))
372.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.2s

Counts
135 → 135
Iterations

Useful iterations: 2 (311.0ms)

IterNodesCost
01792045
14211897
214451617
done50001617

prune471.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.4b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
5.0b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
15.4b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite725.0ms

Algorithm
rewrite-expression-head
Rules
416×add-exp-log
343×prod-exp
84×pow-to-exp pow-exp
52×add-cbrt-cube
43×div-exp
29×cbrt-unprod
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity associate-*r*
9×associate-*l*
6×pow1 unpow-prod-down
5×cbrt-undiv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac *-commutative associate-/l*
2×sqr-pow
1×frac-2neg pow-prod-down clear-num associate-/r* div-inv
Counts
4 → 194
Calls
4 calls:
48.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
286.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
106.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
265.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series1.5s

Counts
4 → 12
Calls
4 calls:
168.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
453.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
533.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
356.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify1.3s

Counts
206 → 206
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02115143
15453013
221092569
done50002565

prune423.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.3b

localize20.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
0.4b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
15.4b
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

rewrite317.0ms

Algorithm
rewrite-expression-head
Rules
466×add-exp-log
382×prod-exp
90×pow-to-exp pow-exp
58×add-cbrt-cube
52×div-exp
34×cbrt-unprod
8×associate-*l*
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×cbrt-undiv
5×pow1
3×expm1-log1p-u unpow-prod-down times-frac log1p-expm1-u associate-/l* add-log-exp
2×associate-*r* *-commutative
1×frac-2neg pow-prod-down clear-num associate-/r* div-inv sqr-pow
Counts
3 → 184
Calls
3 calls:
54.0ms
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
114.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
133.0ms
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

series922.0ms

Counts
3 → 9
Calls
3 calls:
202.0ms
(* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))
402.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x))))
317.0ms
(* (pow cos 2.0) (* (* x (pow sin (/ 2.0 2))) (* (pow sin (/ 2.0 2)) x)))

simplify1.2s

Counts
193 → 193
Iterations

Useful iterations: 2 (420.0ms)

IterNodesCost
01885240
14803102
218642616
done50002616

prune287.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.9b

localize34.0ms

Local error

Found 3 expressions with local error:

0.4b
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
4.9b
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
11.9b
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

rewrite306.0ms

Algorithm
rewrite-expression-head
Rules
455×add-exp-log
371×prod-exp
89×pow-to-exp pow-exp
58×add-cbrt-cube
53×div-exp
33×cbrt-unprod
8×associate-*l*
7×cbrt-undiv add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×pow1
3×expm1-log1p-u unpow-prod-down times-frac log1p-expm1-u associate-/l* add-log-exp
2×associate-*r* *-commutative
1×frac-2neg pow-prod-down clear-num associate-/r* div-inv sqr-pow
Counts
3 → 182
Calls
3 calls:
116.0ms
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
122.0ms
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
42.0ms
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

series1.1s

Counts
3 → 9
Calls
3 calls:
427.0ms
(/ (cos (* 2.0 x)) (* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x)))
376.0ms
(* (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))) (* (pow sin (/ 2.0 2)) x))
308.0ms
(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

simplify1.3s

Counts
191 → 191
Iterations

Useful iterations: 2 (439.0ms)

IterNodesCost
01915082
15103288
219102764
done50002764

prune304.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.5b

regimes514.0ms

Accuracy

0% (2.2b remaining)

Error of 6.7b against oracle of 4.5b and baseline of 6.7b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01632
12032
done2032

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.4s9132×body80valid
994.0ms804×body1280valid
640.0ms977×body640valid
193.0ms551×body320valid
63.0ms282×body160valid